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35. Solutions to Exam Review Pre-Calculus 40s Old Exam QuestionsPage 54 Marking Guide—Pre-Calculus Mathematics (40S)—January 2005SolutionMethod 1( )( )( )22221 sin 1 sinLHS1 sin 1 sin2cos2sec2 tan 12tan 2 RHSq qq qqqqq+ + -=- +=== += + =Method 24 marks1 mark for common denominator1 mark for identity1 mark for identity1 mark for identity½ mark½ mark½ mark forfactoring½ mark forsimplifying1 mark for commondenominator1 mark for identity221 1LHS1 sin 1 sin1 sin 1 sin1 sin2cosLHS RHSq qq qqq= +- ++ + -=-==( )222 22 22 222 2222sinRHS 2cos2sin 2coscos cos2sin 2coscos2 sin coscos2cosqqq qq qq qqq qqq= += ++=+==4 marks
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53. Solutions to Exam Review Pre-Calculus 40s Old Exam Questions113.114.Page 18 Marking Guide—Pre-Calculus Mathematics (40S)—January 20054 2 13 7x x+ +=Solution( ) ( )( )4 2 1log3 log74 log3 2 1 log7log3 4log3 2 log7 log7log3 2 log7 log7 4log3log3 2log7 log7 4log3log7 4log3log3 2log70.877x xx xx xx xxxx+ +=+ = ++ = +- = -- = --=-=Note(s):·· if brackets are omitted in the second step, but assumed to be there, deduct ½ mark· the final answer must be correct to at least 3 decimal places3 marks½ mark for taking the log of both sides½ mark for isolating and factoring x½ mark for consistent answerlog3 0.477 121 ln3 1.098 612log7 0.845 098 ln 7 1.945 910= == =½ mark for log theorem½ mark for solving for x½ mark for distributing
54. Solutions to Exam Review Pre-Calculus 40s Old Exam Questions115.116.Question No. 35Outcome: D1, B3State the range of the function ( ) 2 xf x -= .Answer( )0, OR 0y¥ > 1 mark
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67. Solutions to Exam Review Pre-Calculus 40s Old Exam Questions150.151.152.153.Question No. 31Outcome: B1The graph of 24 5y x x= - - crosses the x-axis at 1 and 5.-Where does the graph of ( ) ( )210 4 10 5y x x= + - + - cross the x-axis?Answer11, 5- -1 mark½ mark for each correct answer
68. Solutions to Exam Review Pre-Calculus 40s Old Exam Questions154.155.Marking Guide—Pre-Calculus Mathematics (40S)—January 2005 Page 43The graph of the function ( ) 5sinf x x p= + touches the x-axis once in the interval [ ]0, 2p .State a possible value of p.Answer5 or –5 1 mark
69. Solutions to Exam Review Pre-Calculus 40s Old Exam Questions156.Marking Guide—Pre-Calculus Mathematics (40S)—January 2005 Page 67Question No. 49Outcome: B1, B5Solutiona) ( )3y f x= + b) ( ) 2y f x= -Note(s):· in a) deduct ½ mark for one incorrect point· in b) deduct 1 mark if they are done in the wrong order1 mark 2 marks1 mark for absolute value1 mark for vertical shiftyx(1, 3)(-2, 3)(-7, -2)yx(-4, 0)(-2, -2)(1, 1) (4, 1)2 marks1 mark
70. Solutions to Exam Review Pre-Calculus 40s Old Exam Questions157.Page 64 Marking Guide—Pre-Calculus Mathematics (40S)—January 2005b) ( )2y f x=c) ( )y f x= -d) ( )y f x= -Solutiona) b)c) d)4 marksx-3 3yx21.5-1.5yx43-3yx-2-3 3yx-3 32
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